Good afternoon, gentlemen.
I was looking through the forum and found this bit in the post with features description of ColourSpace by Ted @ConnecTED:

"4) Internal calibration functions for projectors
ColourSpace HTL supports JVC AutoCAL (using third-party files). X-Rite meters can be used to perform the AutoCAL instead of using Spyder.
Sony projectors have internal 1D LUT.
ColourSpace HTL is supporting the 1D LUT generation (1024 grayscale steps) for Sony software, so you can use ColourSpace to take measurements, generate 1D LUT and then upload it with Sony software."

I suppose I can guess how to export the LUT in Sony format after generation and then import it into the PJ with Sony's software. But I never found any detail on how to create a 1D LUT in ColourSpace for this purpose. Particularly:
1. What patchset(s) should be used for this task? (Any specific greyscale points for Sony? Any specific points for particular model (mine is 870ES)? Where/how could I get/create/purchase them?)
2. What would be the best options to generate patterns for measurements - direct HDMI to PJ, MadVR Envy as TPG or should I get Pi to succeed?
3. How do I generate such 1D LUT in ColourSpace after having done measurements? Should I just use the regular 3D LUT generation option or any specific steps to make it compatible with Sony?

Also a question about the pre-calibration patterns - is it possible to generate the brightness and contrast flashing bars patterns through MadVR Envy when using it as TPG or it is incompatible with those?

There does not seem to be many Sony users/owners here, but any knowledge and experience would be much appreciated. Thank you.

In brief, you can proceed as follows.
Step 1:
Let the projector warm up and set the gamma of the projector to "OFF" (important!!).
Step 2
Use the gain control of the projector to set the white point of the projector as close as possible to D65.
Step 3
Take the "Grey Ramp RGBCMY Large+" measurement with ColourSpace and save it.
It does not matter which pattern generator you use.
Step 4
Use ColourSpace to create and save a 3D Lut ("Fit Space" method).
Step 5:
In ColourSpace, export the Lut you have just created in Sony format "1D Sony_10bits (*.ldt)" as an RGB-corrected gamma curve.
Step 6:
Use the Sony ImageDirector 3.1 program to load the gamma curve into the projector.

Thank you, @Omardris

I'll give it a try. I assume setting the gamma correction to OFF implies that this LUT will be used as a baseline for all gamma settings of the PJ. Am I correct? I would still need to some target for this LUT, I suppose it should be 2.2? I think I've read somewhere that gamma OFF setting in the Sony means 2.2 in reality.

Yes, the Gamma OFF setting corresponds to Gamma 2.2.